Development of a Kinetic Model for Modeling the Industrial VGO Hydrocracker Accompanied By Deactivation

Transcription

1 INTERNATIONAL JOURNAL OF CHEMICAL REACTOR ENGINEERING Volume Article A81 Development of a Kinetic Model for Modeling the Industrial VGO Hydrocracker Accompanied By Deactivation Azita Barkhordari Shohreh Fatemi Mahdi Daneshpayeh Hossain Zamani University of Tehran, barkhordary@ut.ac.ir University of Tehran, shfatemi@ut.ac.ir University of Tehran, m.daneshpayeh@gmail.com National Iranian Oil Company, hzamaninioc@yahoo.com ISSN Copyright c 2010 The Berkeley Electronic Press. All rights reserved.

2 Development of a Kinetic Model for Modeling the Industrial VGO Hydrocracker Accompanied By Deactivation Azita Barkhordari, Shohreh Fatemi, Mahdi Daneshpayeh, and Hossain Zamani Abstract Two types of kinetic modeling, continuous and discrete lump model were studied and compared in this research in order to model the industrial scale VGO hydrocracking process. The experimental data obtained from a pilot-scale fixed bed reactor over Ni-Mo/Silica-Alumina catalyst in a wide range of operating conditions was used for prediction and tuning the kinetic parameters using Genetic algorithm. In this study, the discrete lump model with four parallel reactions to four lumped products showed more convergence to the experimental data than the continuous lump model. Afterward, the discrete kinetic model was used to simulate the vacuum gas oil (VGO) industrial hydrocracking reaction accompanied by catalyst deactivation. The activity of the catalyst was taken as a time dependent variable and the first year of operational data were used to derive the deactivation parameter. The refinery test runs spanning over the last two and half years of operation were used to validate the model and interpret the simulation results. A comparison between the industrial and the predicted data showed that there is a good agreement between them and the presented model provides a reasonable fit to estimate the product yields of LPG, naphtha, kerosene, diesel. KEYWORDS: hydrocracking, catalyst activity, discrete kinetic model, genetic algorithm The authors would like to thank the research vice president of National Iranian Oil Refining and Distribution Company, for the support.

3 Barkhordari et al.: Modeling of VGO Hydrocracker 1 1. Introduction The environmental regulations to improve the quality of petroleum fuels have led to development of hydrocracking process as the second important refining process. Hydrocracking is a catalytic cracking process for the conversion of complex feedstocks, such as vacuum gas oils, into valuable products such as LPG, naphtha, kerosene and diesel, Valavarsu et al. (2005). As the demand for light fuels is going to increase rapidly, the yields and quality of hydrocracking products have to be further improved in meeting the future demands, Rana et al. (2007). There are many process variables and catalyst formulations required to approach to the optimal conditions of a hydrocracker to improve the liquid yield, type and quality of products and catalyst life. In research and development of hydrocracking process, kinetics and process modeling of the complex hydrocracking reactions has become vital. According to the great variety of feed components and complex reactions, the rigorous kinetic modeling of individual reactions is very difficult, complicated and useless in commercial hydrocracking process simulation. An alternative approach is to consider the reaction mixture as the lumped psedue-components which can be specified in terms of physical properties such as ASTM boiling point, molecular weight ranges, carbon numbers, solubility class fractions, and other structural characteristics. Kinetic lumped models have been classified into two categories; the continuous lumped and discrete lump models, Ancheyta et al. (2005). Astarita and Ocone (1988) proposed lumping of nonlinear kinetics described by a continuous distribution function. The kinetic behavior of the mixture was governed by functional-differential equations. Astarita (1989) analyzed the lumping of reactions with non-linear kinetics in a continuous mixture. He showed that the apparent overall order of the reaction depends on the initial concentration distribution and the kinetic parameters. Chou and Ho (1988) proposed a continuum theory of lumping when the kinetics governing the reactions is nonlinear. They formulated the model equations as a function of reactivity. Application of continuum theory of lumping has been described by Laxminarasimhan et al. Cicarelli et al. (1992) investigated the kinetic modeling of catalytic hydrocracking and hydrodenitrogenation of bitumen in terms of a continuous lumping model. They used a novel distribution function to determine the fractional yield distribution of species and formulated integrated differential equations to obtain yields of various fractions as a function of reactor residence time. Extensions of the laxminarasimhan et al. (1996) model, in which the reactions mixture was divided into continuous mixtures of paraffinic, naphthenic and aromatics component, have been published by Basak et al. (2004). Ashuri et al. (2007) developed a continuous lumping model for kinetic analysis of Published by The Berkeley Electronic Press, 2010

4 2 International Journal of Chemical Reactor Engineering Vol. 8 [2010], Article A81 hydrocracking and hydrodenitrogenation reactions. They used the continuous model with five adjustable parameters to describe hydrocracking reactions. The discrete lumping approach was suggested by Stangeland (1974) to introduce a better and simpler approach for modeling hydrocracking kinetics. He developed a utilizing only three parameters for the estimation of product yields of hydrocracking unit. Apart from its simplicity, the assumption of first order kinetics is the main advantage of this model. Krishna and Sexena (1989) suggested a different approach, in which, they considered hydrocracking to be analogous to axial dispersion. Aboul-Gheit (1989) proposed that VGO reacts to form gases, gasoline and middle distillates. The model had eight kinetic parameters that were estimated by experiments performed in a fixed-bed plug flow micro reactor. Anchyeta et al. (1999) proposed a five-lump kinetic model for catalytic cracking of gas oil in which the deactivation of catalyst was considered as an exponential law with one decay parameter depending on the time-on stream Callejas and Martinez (1999), studied the kinetics of Maya residue hydrocracking. They used a first-order kinetics scheme involving three-lump species: atmospheric residuum, light oils and gases. Aoyagi et al. (2003) studied the kinetics of hydrocracking and hydrotreating of conventional gas oils, coker gas oils, and gas oils derived from Athabasca bitumen. They considered a three-lump model consisting of gas oil, hydrocracking products and hydrotreating products with five kinetic parameters. Sanchez et al. (2005) proposed a five-lump kinetic model with ten kinetic parameters for moderate hydrocracking of heavy oils. Ancheyta et al. (2005) reviewed discrete lump kinetic modeling of hydrocracking. Bahmani et al. (2007) used three-lump kinetic model to maximize naphtha and diesel yields of an industrial hydrocracking unit with minimal changes. Balasubramanian and Pushpavanam (2007) developed a discrete lump kinetic model from continuous kinetics using carbon number and true boiling point as the basis to characterize the hydrocarbon cuts. Various technologies such as fixed-bed, moving-bed or ebullated-bed reactors are available for hydroprocessing of heavy oil fractions, Rana et al. (2007). The major selection criterion between each type of technology is based on catalyst deactivation rate, Sie (2001), which depends on the contents of metals and asphaltenes in the feed since products formed during their removal are known as catalyst deactivating species. In the hydrocracking process, the catalyst deactivates during normal operations, Spare (1997). Among all the commercially proven technologies for heavy fraction hydroprocessing, those using fixed-bed reactors in series loaded with catalysts with different functionalities are the most common process configurations, Furimsky (1998). The advantages of using fixedbed reactors are the relative simplicity of scale-up and operation; and the way that the reactors operate in downflow mode, with liquid and gas (mainly hydrogen) flowing down over the catalytic bed. The main disadvantage of fixed-bed reactors

5 Barkhordari et al.: Modeling of VGO Hydrocracker 3 is the loss of catalyst activity over time as a result of premature catalyst deactivation which reduces drastically the length of run, Sie (2001). To design and simulate the behavior of heavy oil upgrading processes at commercial scale, adequate reactor modeling tools are required. The objective of this work is development of a kinetic model based on experimental data, which accounts for major VGO hydrocracking reactions including deactivation of the catalyst by coking, capable of describing the behavior of both pilot and industrial scale reactors. Two models, continuous and discrete lumping are studied and suggested for kinetically modeling the commercial scale of hydrocracking unit. Pilot scale data are used to find the best model fitted to the actual results and the preferred model has been chosen for the industrial scale modeling of Bandar- Abbas hydrocracking unit. 2. Modeling 2.1. Kinetic modeling Two different lump kinetic models were employed to gas oil hydrocracking reaction, continuous and discrete lumping. The models were studied and fitted to the same experimental data to be able to describe better kinetic model for gas oil hydrocracking process. These models are explained in the following sections Continuous lumping The continuous lumping model, used in this study, is the model proposed by Laxminarasimhan et al. (1996). In this model the hydrocarbon mixture is described as a continuous mixture using the TBP (True Boiling Point). The TBP curve is converted into a distribution function with the weight percent of any component as a function of the normalized boiling point, θ, which is defined as: TBP TBP = TBP TBP L θ (1) H L where, TBP H and TBP L represent the highest and the lowest boiling points of the components in the mixture, respectively. Eq. 2 shows the proposed relationship between the first order rate constants, k, and θ. k k max = θ 1/α (2) Published by The Berkeley Electronic Press, 2010

6 4 International Journal of Chemical Reactor Engineering Vol. 8 [2010], Article A81 where α is a model parameter and k max is the rate constant of the species with highest TBP. The mass balance for the component with reactivity of k is represented by: dc( k, t) dt kmax = kc( k, t) + p( k, K ). K. c( K, t). D( K ). dk (3) k where c (k, t) is the concentration of the component with reactivity of k, p (k,k) is a yield distribution function for formation of the component with reactivity of k from cracking of component with reactivity of K and D(k) is the species type distribution function given by: N. α k α 1 D ( k) = α (4) kmax where N is the total number of components in the mixture. The proposed form of the p (k, K) function is given by: p( k, K) = 1 a0 2 [exp [{( k / K) 0.5}/ a1] A + B] S. 2π 0 (5) where A, B and S 0 are defined as: 2 A = exp{ (0.5/ ) } (6) a 1 B = δ { 1 ( k / K )} (7) S 0 K 1 2 a0 = [exp [{( k / K ) 0.5}/ a1] A + 2π 0 B]. D( k) dk (8) The above model has five parameters namely, k max, α, a 0, a 1 and δ. Implementing the model in the CSTR design equation would result in the following expression: kmax C0 ( k) + τ p( kk, ). KCK. ( ). DK ( ). dk (9) k Ck ( ) = 1+ kτ

7 Barkhordari et al.: Modeling of VGO Hydrocracker 5 where C 0 (k) and C (k) are the concentration of the component with reactivity of k in the feed and products, respectively. In a plug flow reactor it is necessary that the calculated concentrations over infinitesimal δt elements satisfy the residence time of the reactor. As the δt elements are smaller, more calculations are needed but the results are more accurate and show less deviation from an ideal plug flow reactor. The concentration of components with reactivity between k 1 and k 2, C 1,2 can be obtained by the following equation: 2 C = C( k). D( k). dk (10) 1,2 k k 1 Eq. 9 is first solved for the heaviest component, component N, with corresponding reactivity, k max, which is only converted to lighter components during hydrocracking reactions: C( k max C0( kmax) ) = (11) 1+ k.δt max Calculation of the concentration of other components would then proceed from component N-1 downward. An optimization method is needed to estimate the model parameters using an objective function defined as the sum of square deviations between predicted and experimental concentration of each boiling fraction in the products including cuts of LPG, Naphtha, Kerosene, Diesel and VGO Discrete lumping Various discrete lumping models are studied for hydrocracking kinetic reaction. In this work, a simple network of four parallel reactions has been introduced for the main lump- products of LPG, Naphtha, Kerosene and Diesel. The reaction network is shown in Fig. 1. Cracking rates are assumed to follow first order kinetics, Qader and Hill (1969) and are listed in Eq. 12 to 16. Published by The Berkeley Electronic Press, 2010

8 6 International Journal of Chemical Reactor Engineering Vol. 8 [2010], Article A81 Feed k 1 k 2 k 4 k 3 Diesel Kerosene Naphtha LPG Fig. 1. Kinetic reaction model of discrete lumping Feed = ( k + k2 + k3 + k4) y Feed r 1 (12) Diesel 1 yfeed = k01exp( E1 / RT yfeed (13) r = k ) Kerosene 2 yfeed = k02exp( E2 / RT yfeed (14) r = k ) r = k ) Naphtha 3 yfeed = k03exp( E3 / RT yfeed (15) r = k ) LPG 4 yfeed = k04exp( E4 / RT yfeed (16) where y feed is the mass fraction of feed in the mixture. The mass balance of each pseudo-component in the packed bed reactor is written from the plug flow assumption as following equation: (17) dy i ri dτ =± where i may refer to any lump product or VGO as the feed, τ is the residence time and r i is the ith rate equation which is expressed by the unit of ith mass fraction per time. The industrial catalyst is a macroporous material with small spherical particles compared to the reactor dimensions and the mass transfer resistances can be ignored in this case study. The mentioned kinetic network was applied to predict the yield of each lump at four space times, and various temperatures. The kinetic parameters were optimized by minimization of the square of difference

9 Barkhordari et al.: Modeling of VGO Hydrocracker 7 between the calculated yields by the model and the experimental yields determined by pilot experiments with fresh catalyst Catalyst deactivation Hydrocracking catalyst deactivates during the operation because of coke formation, poison deposition and solid state transformation. Coke seems to have a strong effect on the hydrogenation and has a much stronger effect than others on the cracking activity, Furimsky (1998). To compensate catalyst deactivation, it is required to increase the process temperature until the product yields are stabilized. Coking affects the main kinetic reactions by a deactivation function. Ancheyta et al. (2000) proposed an exponential decay of catalyst activation with time (t c ) which can be used for industrial data. In this work an exponential function is used to represent the catalyst activation coefficient with the time on stream: ϕ = Exp( k d tc) (18) There is a parameter (k d ), in Eq. 18 which should be predicted using experimental industrial data during a long period of time Parameter estimation Mathematical modeling of the reaction network, presented in the previous section, involves unknown parameters which they are usually determined by an optimization technique. Applying classical gradient based algorithms may achieve to the local optima and finding the appropriate initial estimates of the parameters is difficult to converge to the global optima, Marquardt (1963). To overcome these limitations, various approaches based on the evolutionary algorithms have been recently used for determining the kinetic parameters by optimization. One of these evolutionary algorithms for kinetic reaction modeling is the Genetic Algorithm, Fatemi et al. (2005). In the present study, decimal Genetic Algorithm (GA) was implemented to predict the kinetic parameters of the reactions. The flowchart of the algorithm is shown in Fig. 2 and its general procedure is described below. The solution procedure starts with a randomly set of candidate solutions within their defined range and mapping called population and evaluate the fitness of each individual in the population which is called a chromosome. A population with 100 chromosomes was selected in this study. The fitness function is defined as the sum of squares of the error of each point data from the model results. Published by The Berkeley Electronic Press, 2010

10 8 International Journal of Chemical Reactor Engineering Vol. 8 [2010], Article A81 Fitness = = = i i E 1 ( M icalc M ) 2 i exp (19) Start Generate initial population Find fitness of each chromosomes Select mates Mating Mutation Conversion check End Fig. 2. Flowchart of the genetic algorithm where E is the number of experimental points. The next step is Selection in which two parents form population are chosen to create the next generation and make a new chromosome called offspring through the mating and mutation. The offsprings substitute with a percentage of the chromosomes (50% in this study) with higher fitness. There are many different strategies for this selection process and they all need to ensure that the fitter candidates are more likely to be included into the breeding population, but still allow exploration of large areas of the parameter space, Maeder et al. (2004). In this study, an elitist method, Lucasius and Kateman (1994); and Maeder et al. (2003), was chosen to select parent from only a percentage of the best individual. In the mating section two chromosomes of current generation mate were selected using crossover operator to make new offsprings through following equations: Offspring β ( Parent (20) 1 = Parent1 + 1 β) 2

11 Barkhordari et al.: Modeling of VGO Hydrocracker 9 Offspring β ( Parent (21) 2 = Parent2 + 1 β) New offsprings were modified using uniform mutation operator, in Eq. 22, with probability 15% to make new population for next generation, Maeder et al. (2004). Mutated Gen 1 = Orginal gen 1 ξ ) + ξ ( a i b ) (22) ( i where ξ is a positive random number less than one, a i and b i are the upper and lower bound of the variable. After mutation, the fitness associated with the offsprings is calculated and the optimization process is iterated. Genetic algorithm was continued with 1000 iterations and interrupted after there was not any convergence improvement in objective function. 3. Experimental data 3.1. Pilot plant data The experimental data used for kinetic parameter estimation and comparison of two models (continuous and discrete) were taken from pilot plant experiments, El- Kady (1979), in which hydrocracking of vacuum gas oil was carried out in an isothermal tubular packed bed reactor working at a wide range of operating conditions, such as reaction temperature of 390, 410 and 430 C, space times of 0.4, 0.667, 1 and 2 hr at a constant pressure of 10.3 MPa. The reaction was conducted using a bifunctional Ni-Mo/silica-alumina catalyst, which was replaced by fresh catalyst after a few operations. With catalyst replacement, the authors were assured it works in a regime in which catalyst deactivation can be neglected. A more detailed description of the experiments is given elsewhere, El-Kady (1979). After tuning the kinetic parameters and choosing the best fitted model, continuous or discrete, simulation of the industrial hydrocracking process could be performed Industrial plant data To determine the deactivation effect on catalyst performance, the industrial refinery data is required. The industrial plant data was received from Isomax unit of Bandar Abbas oil refinery during three and a half years of operation. A simple schematic of the plant is shown in Fig. 3. Published by The Berkeley Electronic Press, 2010

12 10 International Journal of Chemical Reactor Engineering Vol. 8 [2010], Article A81 Fig. 3. Schematic diagram of two-stage hydrocracking process In this plant there are two reactors in series, and each reactor is injected by hydrogen make up to keep hydrogen at excess ratio and to delay catalyst coking. Each reactor is divided into two sections; the first section of the first reactor is filled with Ni-Mo and the other sections filled with Ni-W on silica-alumina catalysts. It was found that Ni-Mo had relatively similar activity to Ni-W, Walid (2004). As the reactors operate at adiabatic condition, the bed temperature varies from 405 to 423 C, first to the end run temperature, therefore WABT 1 (weight average bed temperature) was utilized in the simulation which was considered as a constant working temperature for isothermal conditions and it was calculated from measured temperatures at each part of the bed using 15 thermocouple readouts along the column. The overall space time of the process is kept constant and equal to hr. The outlet product was splited into five lumps of LPG, naphtha, kerosene, diesel, and VGO, which were considered for validation of the model in industrial scale. The feed, catalyst and reactor specifications, the yields of lump products at initial time (WABT= 405 C) and final time (WABT= 423 C) of the process are listed in Tables 1, 2, 3 and 4, respectively. 1 n WABT = wt, where n is the number of thermocouples in the axial direction, w i, weight i= 1 i i fraction of the catalyst and T i is the temperature of ith fraction of the catalyst bed

13 Barkhordari et al.: Modeling of VGO Hydrocracker 11 Table 1. Physical and chemical properties of the industrial scale feedstock Property Feedstock Sp. Gr C 4.8 S, wt% 1.57 C7 insoluble wt% 0.12 Distillation ASTM D-86 IBP, C Vol%, C Vol%, C Vol%, C Vol%, C Vol%, C Vol%, C Vol%, C Vol%, C 506 Lumps of feed comp. (wt%) Diesel %10 VGO %90 Flow rate (m 3 /hr) H 2 /HC (m 3 /m 3 ) 2150 Table 2. Specification of the industrial scale catalysts NiO-WO Catalyst 3 /SiO 2 -Al 2 O 3 NiO-MoO 3 /SiO 2 -Al 2 O 3 (first section) Shape TRILOBE (extrudate) TRILOBE (extrudate) Size diameter (1.3 mm) length (3-5 mm) Diameter (2-3 mm) length (3.8-6 mm) Bulk Density (kg m -3 ) Surface Area (m 2 gr -1 ) Pore Volume (cc gr -1 ) Published by The Berkeley Electronic Press, 2010

14 12 International Journal of Chemical Reactor Engineering Vol. 8 [2010], Article A81 Table 3. Commercial Reactor s conditions Number of reactors 2 Initial inlet temperature( C ) 380 Final inlet temperature( C ) 395 Reactor inlet pressure (Mpa) Bed 1, section 1 Bed 1, section 2 Bed 2, section 1 Bed 2, section 2 diameter ( m) (internal-external) Length (2.115 m) Weight(15540 kg) diameter ( m) (internal-external) Length (4.300 m) Weight(32375 kg) diameter ( m) (internal-external) Length (5.215 m) Weight(38850 kg) diameter ( m) (internal-external) Length (5.670 m) Weight(42698 kg) Table 4. The yield of products at initial and final WABT (405, 423 C) of the process, at the space time of hr Products LPG Naphtha Kerosene Diesel Yield (at the initial WABT) Yield (at the final WABT) The psedue-components studied in discrete lump kinetic model and their distillation ranges are presented in Table 5. Table 5. Components properties Cut No. Component Distillation Range 1 LPG 0-39 C 2 Naphtha C 3 Kerosene C 4 Diesel C 5 VGO 380 C+

15 Barkhordari et al.: Modeling of VGO Hydrocracker Results and Discussion The parameters of the kinetic models, i.e. continuous and discrete lumping, were estimated using the experimental data in various space times of the pilot scale. Twenty data of five lumps at four space times (0.4, 0.667, 1 and 2 hr) were used to estimate the kinetic parameters at a constant operating temperature. Since the WABT of the industrial reactor was varied from 390 to 430 C, initial to final step, the pilot data were analyzed at different temperatures of 390, 410 and 430 C for prediction of the intrinsic kinetic parameters at various temperatures. The kinetic parameters are temperature dependent, as denoted by the Arrhenius equation. The parameters were first estimated and optimized by GA using the fitness function of sum of squared error between the experimental and calculated yields of product. In the next stage, two models were compared with each other and the best model was chosen according to the model precision. Additionally, catalyst deactivation was considered using industrial scale data for developing a real hydrocracking kinetic model Continuous lumping The results of 12 test runs are observed at various temperatures and space times, in Table 6. At each run, the cumulative yield of the lump components are implemented in the lump kinetic model for prediction of the five kinetic parameters. The kinetic parameters are optimized by GA at each temperature and reported in Table 7. Table 6. Experimental yields of each lump component at 12 test runs, El-Kady (1979) Space Time Temprature LPG Naphtha Kerosene Diesel VGO Published by The Berkeley Electronic Press, 2010

16 14 International Journal of Chemical Reactor Engineering Vol. 8 [2010], Article A81 Table 7. The predicted parameters of the continuous lumping model Temperature ( C) K max Α δ a 0 a The parity plot of the error versus the product yields of the model at various space times and temperatures of 390, 410 and 430 C is presented in Fig. 4. (Yieldexp. - Yieldmodel) LPG Kerosene VGO Naphtha Diesel Yield model Fig. 4. The residual (Y exp -Y model ) versus yield of products in continuous lumping model at T=390, 410 and 430 C, space time= 0.4, 0.667, 1 and 2 hr As can be observed, the residual error of heavier cuts is more than the lighter ones because heavy lump cuts are obtained by summation of the lighter fractions, then the occurred error is cumulated step by step for prediction of the light to heavy cuts. The major drawback of this model is that it may show significant error in yield predictions of various products at higher severities Discrete lumping The experimental data of Table 6 were employed for discrete lump kinetic modeling and they were used for prediction of the four kinetic parameters in

17 Barkhordari et al.: Modeling of VGO Hydrocracker 15 discrete lumping model. Firstly, four kinetic parameters were estimated and used in the rate equations of 12 to 16 and they were employed in equation 17, as mass balance equation of each lump component. The mass fraction of each component (yield) was calculated along the bed and the outlet yields were compared with actual results of Table 6. Optimization of the kinetic parameters was carried out by GA after solving the mass balance equations in each temperature and minimization of equation 19 as the objective function. The optimized kinetic parameters are reported in Table 8 at three different temperatures. By fitting Lnk i versus 1/T, the constants of Arrhenius equations are calculated and reported in Table 9. The parity plot of the error versus the model products yields can be observed in Fig. 5. Table 8. Optimized kinetic parameters of discrete model at each temperature Temperature( C) k 1 k 2 K 3 k Table 9. Arrhenius kinetic constants of the discrete lump model i=lump No. K 0i (1/hr) E i /R ( K) k i = k 0i Exp ( E i / RT ) Published by The Berkeley Electronic Press, 2010

18 16 International Journal of Chemical Reactor Engineering Vol. 8 [2010], Article A81 (Yieldexp. - Yieldmodel) LPG Kerosene VGO Naphtha Diesel Yield model Fig. 5. The error (Y exp -Y model ) versus yield of products by discrete lumping model at T=390, 410 and 430 C and space times; 0.4, 0.667, 1 and 2 hr. As can be observed, discrete lumping model has shown a better fitting than continuous lumping. In contrary to the continuous model, the experimental yield of each lump component is considered independently in discrete model and the error raised from modeling is uniformly dispersed within the whole range of the studied yields. The average absolute relative deviations are determined in all temperatures for the discrete and continuous lumping model and presented in Table 10. The data given in table 10 show that, despite of less number of parameters of discrete lumping method, it provides a better fit compared to the continuous lumping method Catalyst deactivation Table 10. Comparison of relative errors for two models Model * AARD (%wt) Discrete 5.97 Continuous 9.16 N 1 y AARD = N expi y y i= 1 expi modi 100, N = 60 Due to the higher precision of discrete lumping towards the pilot experimental results, it was selected and accompanied with catalyst deactivation for industrial

19 Barkhordari et al.: Modeling of VGO Hydrocracker 17 scale hydrocracking modeling. The activation energies proposed by discrete model were employed directly into the industrial scale modeling. The other kinetic parameters; pre-exponential terms of Arrhenius equation as well as the parameter of deactivation function, were tuned by GA for prediction of the yields of LPG, Naphtha, Kerosene, Diesel and activity coefficient of commercial VGO hydrocracking process. The first run temperature, with 20 data points, was used to obtain all the preexponential kinetic parameters, for the fresh catalyst that is listed in Table 11. The other run temperatures during the first year (48 data-mean average of each month) were used to derive the coefficient of catalyst decay. These parameters are reported in Table 12. The results of the rest of two and a half year operation of industrial scale (40 data- mean average of each three month) were used to validate the simulation results. Table 11. The first runs temperature for the fresh catalyst of industrial scale No. of Run LPG Naphtha Kerosene Diesel Table 12. The tuned pre- exponential kinetic parameters for industrial scale, with the same activation energies obtained from pilot scale. i=lump No. * K 0i (hr -1 ) E i /R ( K) k d * :k i =k 0i Exp(-E i /RT) :φ=exp(-k d t c ) Comparison of experimental and predicted values of the product yields was examined for validation of the model during the rest of two and a half year operating time, and is observed in Fig. 6. As it is observed, this model shows a good prediction of industrial scale data. The total relative error is presented in Table 13, for each lump product. Published by The Berkeley Electronic Press, 2010

20 18 International Journal of Chemical Reactor Engineering Vol. 8 [2010], Article A81 Table 13. The total relative error of the product yields Product AARD (%wt) LPG Naphtha Kerosene Diesel AARD (%wt) = 9.14 Predicted Yeild Wt.% LPG Naphtha Kerosene Diesel Experimental Yeild Wt.% Fig. 6. Comparison of the industrial scale yield and model during the rest of two and a half year The trend of the WABT, φ and the total yield of products with the time of stream is shown in Fig. 7. The three and a half year operation of VGO hydrocracker has shown that catalyst activity drops from 1 to 0.6. As can be observed in this figure, the total yield of products is constant during the time of the process. The resultant products of the VGO hydrocracker of Bandar Abbas Refinery are shown in Fig. 8 during the total three and a half year operation. The yield of each lumped product is presented by the model in this figure which shows a good prediction over the total run time of the process.

21 Barkhordari et al.: Modeling of VGO Hydrocracker Yield φ & Yield φ WABT Temperature ( C) 0.5 deact.coe. Total Yield WABT Stream Time (days) Fig. 7. WABT, φ and total yield versus time. WABT and total yield are presented from the real operational data, activity function is presented by the model Naphtha 25 Product Yeild Wt.% Kerosene Diesel LPG Stream Time (days) Fig. 8. Effect of the stream time on product yield. The curves are derived by the model. The points are presented from the industrial plant. The yield of any lumped products is determined by the model along the bed column at the average temperature of WABT=416 C and after 720 days on stream in Fig. 9. The results of the model and commercial scale are in a good agreement with each other at the outlet of the bed. 0 Published by The Berkeley Electronic Press, 2010

22 20 International Journal of Chemical Reactor Engineering Vol. 8 [2010], Article A81 Component Yield Wt.% Diesel 40 Naphtha 30 Kerosene LPG VGO Lenght of Reactor (m) Fig. 9. The yield of lumped products versus reactor length, at WABT= 416 and after 720 days on stream. The curves are derived by the model. The points are presented from the industrial plant at the end of the bed. 5. Conclusion Kinetics of hydrocracking over industrial catalyst was modeled, using experimental data of a pilot fixed-bed reactor and GA as a parameter optimizer. In order to choose the best reaction model for developing an appropriate kinetic model over the industrial scale process, discrete and continuous lump models were studied and compared. The reaction mixture was considered as five lumps pseudo-components i.e. LPG, Naphtha, diesel, kerosene and VGO. After parameter prediction of both models with appropriate rate equations, the models were discriminated based on experimental data. The results showed that despite of less number of kinetic parameters in discrete model against continuous model, four against five respectively, the discrete lump model with AARD of 5.97% revealed higher precision than the continuous model with AARD of 9.16%. In order to develop the kinetic model to the industrial scale process, the time dependent catalyst activity was considered into the kinetic parameters and commercial yields of a VGO industrial hydrocracking process were implemented to tune the activation function. The catalyst activity was considered as an exponential function of time with one parameter and it was tuned by industrial data. The results indicated that the presented model has reasonable fit with industrial data of VGO hydrocracker of Bandar Abbas refinery and can be used as a generic one for process simulation and optimization of hydrocracking processes.

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